i dont have much time so that i really need help

4. The following data were given in a study of a grou of 1000 subscribers to a certain magazine: In re erence to job, marital status, and education, ther were 312 professionals, 470 married persons, 52 college graduates, 42 professional college gradu ates, 147 married college graduates, 86 marrie professionals, and 25 married professional colleg graduates. Show that the numbers reported in th study must be incorrect. Hinn: Let M. W. and G denote, respectively, th set of professionals, married persons, and colleg graduates. Assume that one of the 1000 person is chosen at random, and use Proposition 4.4 t show that if the given numbers are correct, the P(MUWUG) > 1. 5. If it is assumed that all 52 5 poker hands ar equally likely, what is the probability of being dea (a) a flush? (A hand is said to be a flush if all cards are of the same suit.) (b) one pair? (This occurs when the cards hav denominations a, a, b. c. d, where a, b, c, an d are all distinct.) (c) two pairs? (This occurs when the cards hav denominations a, a, b, b, c. where a, b, and are all distinct.) (d) three of a kind? (This occurs when the card have denominations a, a, a, b, c, where a, and c are all distinct.) (e) four of a kind? (This occurs when the card have denominations a, a, a, a, b.) 6. Poker dice is played by simultaneously rolling dice. Show that (a) P(no two alike) = .0926; (b) Plone pair} = .4630; (c) P(two pair) = .2315; (d) P(three alike] = .1543; (e) P(full house) = .0386; (f) P(four alike) = .0193; (g) P(five alike) = .0008. 7. If 8 rooks (castles) are randomly placed on chessboard, compute the probability that none the rooks can capture any of the others. That